Home
Class 11
MATHS
In any A B C , prove that: =(a^2-b)/2do...

In any ` A B C ,` prove that: `=(a^2-b)/2dot(sinAsinB)/(sin(A-B))`

Text Solution

Verified by Experts

RHS `=(b^(2)-c^(2))/(2). (sinBsinC)/(sin(B-C))`
`=(k^(2)sin^(2)B-k^(2)sin^(2)C)/(2).(sinBsinC)/(sin(B-C))`
`k^(2)(sin^(2)B-sin^(2)C)/(2).(sinBsinC)/(sin(B-C))`
`(sin(B+C)sin(B-C))/(2).(ksinB.ksinC)/(sin(B-C))`
`=1/2bc.sin(B+C).b.c`
`=1/2bc.sin(180^(@)-A)`
`=1/2bcsinA=Delta`=LHS Hence Proved.
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISES 3A|12 Videos

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISES 3B|24 Videos

  • STRAIGHT LINES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|207 Videos

Similar Questions

Explore conceptually related problems

In any A B C , prove that: Delta=(a^2-b^2)/2dot(sinAsinB)/(sin(A-B))

In any DeltaABC , prove that Delta=(a^(2)-b^(2))/2(sinAsinB)/(sin(A-B)) .

In any triangle A B C , prove that: (a^2sin(B-C))/(sinB+ sin C)+(b^2sin(C-A))/(sinC+ sin A)+(c^2sin(A-B))/(sinA+ sin B)=0

In any DeltaABC , prove that : (b^2 - c^2)/a^2 = (sin (B-C))/(sin(B+C))

In DeltaABC , prove that: (a-b)/c=(sin(A-B)/(2))/(cosC/2)

In any A B C , prove that: 2{asin^2C/2+csin^2A/2}=a+c-b

In any triangle A B C , prove that: ("sin"(B-C))/("sin"(B+C))=(b^2-c^2)/(a^2)

In any triangle A B C , prove that: acos((B-C)/2)=(b+c)sin(A/2)

For any triangle ABC, prove that (a-b)/c=(sin((A-B)/2))/(cos(C/2))

In any triangle A B C , prove that: \ asin(B-C)+b sin(C-A)+csin(A-B)=0